SteamBirds is a top-down, turn-based, aeriel dogfighting game with an unusual core mechanic. Each turn, you give orders to your aircraft by moving a pointer that indicates where it will end the turn; the system only lets you drag the pointer to a location the aircraft can reach, so that the turning radius, speed, and ability to accelerate or decelerate is build into the scheme. Elevation, and diving/climbing, are neglected. Guns are fore-mounted, so the trick is to get behind the enemy and stay on their tail.
Some aircraft have special abilities--a turboboost to speed, the ability to do a 180 degree turn, one-turn shields, the ability to spray 'gas' that damages those behind. New abilities are gradually introduced by level.
Presumably in order to avoid having to pay attention to historical realities, the game takes place in a universe in which "cold fusion" was invented in the 19th century, and these are all nuclear-powered, steam-driven aircraft (hence the name). It also seems to be a pretty wretched alternate future; World War II begins with the nuking of Paris.
While far from a sim, it does have a nice balletic feel, imparting a sense, if not the reality, of aerial dogfighting.
The Flash version is free; the mobile versions are not.